| 梁横振动方程反问题的梯度方法 |
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| 引用本文： | 唐元华,黄光远.梁横振动方程反问题的梯度方法[J].中国科学技术大学学报,1988(4). |
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| 作者姓名： | 唐元华 黄光远 |
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| 作者单位： | 中国科技大学
(唐元华)，山东大学(黄光远) |
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| 摘 要： | 本文集中讨论一维弹性悬臂梁的四阶横振动方程及该方程反问题的梯度方法,其识别参数是梁的高度在一维空间上的分布函数。文中首先得到了该方程的简化模型,给出了当其系数为分段常数时方程的稳定的差分算法。在将参数识别问题转化为分布参数系统的系数最优控制问题以后,给出了目标泛函的梯度公式,以及计算机仿真方法。
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| 关 键 词： | 分布参数系统 反问题 目标函数 梯度方法 最优控制 弹性梁振动 变分方法 |
The Gradient Method for Inverse Problem of the Beam Vibration Equation |
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| Tang Yuanhua,Huang Guangyuan University of Science and Technology of China Shandong University.The Gradient Method for Inverse Problem of the Beam Vibration Equation[J].Journal of University of Science and Technology of China,1988(4). |
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| Authors: | Tang Yuanhua Huang Guangyuan University of Science and Technology of China Shandong University |
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| Institution: | Tang Yuanhua;Huang Guangyuan University of Science and Technology of China Shandong University |
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| Abstract: | The differential equation considered in this paper is the transversevibration equation of one-dimension elastic beam. we concentrate our topic onthe new numerical method for the solution of the equation and the inverseproblem (parameter identification) of the equation, the parameter identifiedis the distributed height function of the beam. After deducing the parameteridentification problem to the optimal control problem of distributed para-meter system, the formula for the calculation of criteria gradient is given, byusing the techniques of adjoint-equation and the Chen-Chavent method. Thecomputer calculation procedure both for the solution problem and the inverseproblem are given, which show that the algorithmses are feasible and greatlytime-saving, compared to other methods for the identification problem. |
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| Keywords: | distributed parameter systems inverse problem criteria function gradient method beam vibration equation variational method |
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